System and method for tomography combining single and paired photons

ABSTRACT

Methods and systems for producing an image. Measurement data is obtained for a coincidence photon event, and a line projector function is generated based on the obtained measurement data. Additional measurement data is obtained for a single photon event, and a cone-surface projector function is generated based on the additional measurement data. An image is reconstructed using the generated line projector function and the generated cone-surface projector function. In another example method for producing an image, a measurement is obtained, and a projector function is generated using the obtained measurement. The generated projector function is modified based on an a priori image. An image is reconstructed using the modified projector function.

PRIORITY CLAIM AND REFERENCE TO RELATED APPLICATION

The present application claims the benefit of U.S. ProvisionalApplication Ser. No. 60/931,177, filed May 21, 2007, and U.S.Provisional Application Ser. No. 60/931,178, filed May 21, 2007, under35 U.S.C. §119, which are incorporated in their entirety by referenceherein.

STATEMENT OF GOVERNMENT INTEREST

This invention was made with Government assistance under NationalInstitutes of Health (NIH) Grant Nos. CA119056 and EB003283. TheGovernment has certain rights in the invention.

This application is also related to co-pending application Ser. No.12/154,261, entitled “METHOD AND SYSTEM FOR USING TISSUE-SCATTEREDCOINCIDENCE PHOTONS FOR IMAGING”, filed on even date herewith.

FIELD OF THE INVENTION

The invention relates generally to the field of high-resolution imaging.

BACKGROUND OF THE INVENTION

In tomography, measurements are taken though multiple views of a subject(e.g., human or animal in biomedical applications), and mathematicalalgorithms are used to convert these measurements into three-dimensional(3-D) images of the subject. Such algorithms are referred to astomography image reconstruction algorithms.

Example tomography image reconstruction algorithms can be performed bysuccessive approximation methods, such as iterative maximum likelihood(ML) expectation-maximization algorithms. In an iterative ML algorithm,an image is updated using a gradient-based function at each iteration.The gradient function is calculated using a forward projection function,which describes how the 3-D image maps to the data space.

However, this forward projection is mathematically ill-posed. Forexample, noise in the measurements is amplified by the imagereconstruction algorithm, degrading the image quality. Filtering canreduce the noise, but at the expense of image resolution and contrast.

An example imaging technique is positron emission tomography (PET).Generally, in PET and similar imaging methods, radioactive isotopes areinjected into a subject. Decay of the isotopes (that is, apositron-electron annihilation event) results in photons being emittedfrom inside the animal. In conventional PET, detectors positionedoutside the animal detect emitted photon pairs when they hit thedetectors. These interactions are recorded, including the detectionlocation and the energy. Based on these recorded interactions, an imageof where the radioactive isotope is distributed in the body can beimaged using a tomography image reconstruction algorithm. PET is awidely used clinical imaging procedure for applications such as, but notlimited to, staging and monitoring disease in cancer patients.

Conventionally, emitted photons from a source that are detected incoincidence by the detectors are used to reconstruct the 3-D tomographicimages. So-called true coincidence events are assumed to have occurredsomewhere along the line between two photons detected within a presetcoincidence time window. Thus, a line can be determined between thephoton pair based on the location of the detected photons, and thedetermined lines can be used to construct the image.

However, a large majority of the events detected by the detectors arenot true coincidence events, but rather single photon events. It hasbeen estimated that single-photon events make up about 90% of alldetected events in a human PET system. Conventional PET systems do notuse these single photon events to produce images. Alternate detectordesigns can be used to produce images from single photons. However,single photons do not provide images of the same resolution as that ofcoincidence photons, even though there are more single photon events.Thus, conventional PET systems ignore single photon events, and largeamounts of available information remain unused, reducing thesignal-to-noise ratio of the reconstructed image.

SUMMARY OF THE INVENTION

Embodiments of the present invention provide, among other things,methods and systems for producing an image. In an example method,measurement data is obtained for a coincidence photon event, and a lineprojector function is generated based on the obtained measurement data.Additional measurement data is obtained for a single photon event, and acone-surface projector function is generated based on the additionalmeasurement data. An image is reconstructed using the generated lineprojector function and the generated cone-surface projector function.

In another example method for producing an image, a measurement isobtained, and a projector function is generated using the obtainedmeasurement. The generated projector function is modified based on an apriori image. An image is reconstructed using the modified projectorfunction.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 shows an imaging system according to an embodiment of the presentinvention;

FIG. 2 shows an example individual 3-D detector;

FIG. 3 is a schematic diagram illustrating Compton kinematics for the3-D CZT detector of FIG. 2;

FIG. 4 shows an example imaging method using both single photon eventsand coincidence events, according to an embodiment of the presentinvention;

FIG. 5 shows an example method for determining whether a coincidenceevent or a single photon event is present;

FIG. 6 shows an example method for using an a priori image formulti-collimation events, according to an embodiment of the presentinvention;

FIG. 7 shows an example small animal PET system;

FIGS. 8A-8B show reconstructed images of a phantom with 16 sphericalsources using coincidence data and non-coincident singles datarespectively;

FIGS. 9A-9D show images reconstructed by various methods, where FIG. 9Ashows a reconstructed image using only coincidence data, FIG. 9B shows areconstructed image using simultaneous data channels, FIG. 9C shows areconstructed image using sequential data channels, and FIG. 9D shows areconstructed image using a Bayesian projector approach;

FIGS. 10A-10D show mean reconstructed images, where FIG. 10A shows amean reconstructed image using only coincidence data, FIG. 10B shows amean reconstructed image using simultaneous data channels, FIG. 10Cshows a mean reconstructed image using sequential data channels, andFIG. 9D shows a mean reconstructed image using a Bayesian projectorapproach;

FIG. 11 shows peak-to-valley ratios for four reconstruction methods;

FIG. 12 shows a full width at half maximum (FWHM) of a Gaussian functionfitted to profiles drawn through spheres reconstructed though variousmethods;

FIG. 13 shows an example reconstruction algorithm using a Bayesianapproach, according to another embodiment of the present invention;

FIG. 14 shows an example detector arrangement used in example methodsillustrating the Bayesian approach shown in FIG. 13, with an individualdetector enlarged for clarity;

FIGS. 15A-15B show two digital phantoms of a cylinder and spheres usedin an experiment, where FIG. 15A shows phantom 1 with a 9:1sphere:cylinder activity ratio, and FIG. 15B shows phantom 2 with threecolumns of each size sphere, where the outer columns have a 9:1sphere:cylinder activity ratio, the middle columns have a 5:1sphere:cylinder activity ratio, and the innermost have a 3:1sphere:cylinder activity ratio;

FIGS. 16A-16B show reconstructed images for phantom 1, where FIG. 16Ashows an OS-EM algorithm using only coincidence events forreconstructing the image, and FIG. 16B shows a list-mode OS-EM algorithmused to combine coincidence and single photons;

FIGS. 17A-17B show reconstructed images for phantom 2 with a morerealistic energy resolution model, where FIG. 17A shows an OS-EMalgorithm using coincidence events, and FIG. 17B shows an OS-EMalgorithm using a Bayesian projector for Compton collimation and astandard projector for coincidence events;

FIGS. 18A-18B are plots of sphere signal-to-noise (SNR) vs. contrastratio for different iteration subsets for coincidence reconstruction andcombining coincidence and singles reconstruction using the Bayesianprojector, wherein FIG. 18A shows 5 to 1, 1.5 mm spheres, and FIG. 18Bshows 10 to 1, 1.75 mm spheres; and

FIGS. 19A-19B are plots of sphere SNR versus contrast ratio fordifferent iteration-subsets for coincidence and singles reconstructionusing the Bayesian projector with detector voxel sizes of 0.025, 0.5,and 1 mm, where FIG. 19A shows 5 to 1, 1.5 mm spheres and FIG. 19B shows10 to 1, 1.75 mm spheres.

DETAILED DESCRIPTION

In PET, coincidence events may be used to provide image information byusing coincidence measurements. That is, PET systems conventionallydetermine a line between a pair of detected photons (coincidencecollimation), along which line the position of a decay event in tissueis determined to occur. However, single detected photons have beendiscarded in conventional PET systems, though they provide the largemajority of detected events. Example embodiments of the presentinvention use both single photon events and coincidence photon events toproduce 3-D tomographic images. Single photon events are incorporatedinto the set of usable events via Compton kinematics collimation.

Compton kinematics collimation is an imaging method that uses thekinematics of Compton scatter (Compton kinematics). In a typical exampleof so-called Compton PET, a Compton camera uses a scattering layer andan absorption layer, and produces images from measurements of singlephotons. By recording the position and energy of a Compton interactionin the scatter layer and a photoelectric interaction in the absorptionlayer, the Compton kinematics can position the decay event somewhere ona cone-surface.

In an example of Compton kinematics collimation, the energies andpositions of individual interactions are measured in a 3-D detector andused to calculate the direction of each individual photon. The decayevent is then localized to the surface of a cone based on Comptonkinematics.

However, Compton kinematics collimation conventionally has suffered frompoor angular blurring due to Doppler broadening, energy blurring, andposition blurring. Thus, the reconstructed spatial resolution of Comptonkinematics collimation is limited compared to coincidence collimation.Combining Compton kinematics collimation with coincidence collimation toproduce better images is a challenging problem because of this largeresolution mismatch. According to example methods of the presentinvention, these two measurements can be combined to improve overallimage quality and/or quantification.

Hybrid Compton PET systems using two Compton cameras with coincidencecapability have also been proposed. Such systems are able to performboth conventional coincidence PET imaging and Compton kinematicsimaging. Some three-dimensional (3-D) PET detectors also have theability to function as a coincidence detector and as a Compton camera. A3-D detector can perform coincidence Compton kinematics collimation onsingle photons if it can precisely measure the position and energy ofindividual interactions in the detector.

In an example embodiment of the present invention, a PET system andmethod is provided in which 3-D detectors are used to perform two typesof electronic collimation: coincidence collimation and Comptonkinematics collimation. In this way, the data form different channels,including a coincidence collimation channel and a Compton kinematicscollimation channel. An example reconstruction algorithm combines thesetwo channels to provide image reconstruction and detection and produce a3-D tomographic image. Example embodiments of the present invention alsoaccount for the large resolution mismatch between coincidencecollimation and Compton kinematics collimation.

Using coincidence collimation and Compton kinematics collimation, anexample PET system can image both coincidence photon pairs and singlephotons. Thus, example methods and systems can recover many additionalevents not used by current PET methods, increasing the statistics of thedata set and potentially improving the image quality and/orquantification. Example embodiments also provide both benefits ofcoincidence photons (e.g., higher resolution) and single photons (highersignal-to-noise ratio).

In an example method for producing an image of a subject according tothe present invention, measurement data is obtained for a coincidencephoton event, and a line projector function is generated based on theobtained measurement data, providing a coincidence collimation channel.Additional measurement data is obtained for a single photon event, and asingle photon projector function, such as a cone-surface projectorfunction, is generated based on this additional measurement data toprovide a Compton kinematics collimation channel. By combining the datafrom the coincidence collimation channel and the Compton kinematicscollimation channel, an image of the subject is reconstructed using thegenerated line projector function and the generated cone-surfaceprojector function.

An example projector function for coincidence photons is the linebetween the two detectors that recorded the photons. An example Comptonkinematics cone-surface projector function estimates the incomingdirection of photons using Compton kinematics within the detector.

More particularly, to calculate a Compton kinematics cone-surfaceprojector function, multiple interactions in the detector for a singlephoton event are detected, including the interaction position andenergy. The incident angle on the photon can be estimated using themeasured interaction position and energy, for example, for the first twointeractions in the detector. A cone-surface projector function is thenformed. However, more than two interactions may be used.

To calculate the projection function for coincidence photons, an exampleimaging system and method may calculate a line projector function.Methods for calculating a line projector function for coincidence eventswill be understood by those of ordinary skill in the art.

These separate data channels can be combined using any of varioustechniques in so-called multi-channel tomography for imagereconstruction. The coincidence events form one data channel withhigh-reconstructed spatial resolution. The non-coincident singles eventsform a second channel with low-reconstructed spatial resolution. Theobjective then becomes combining these channels to produce an image withsuperior quality in terms of contrast, resolution, and/orsignal-to-noise ratio. Nonlimiting example reconstruction methods areprovided according to embodiments of the present invention, includingusing simultaneous data channels, using sequential data channels, andusing a Bayesian projector function. It will be understood thatvariations on the algorithms described herein are possible according tovarious embodiments of the present invention.

In an example method using simultaneous data channels, a data vector isformed including a combination of coincidence and non-coincident singleevents, and a system matrix is formed using discrete approximations ofreconstruction models for the two channels. In an example use ofsequential data channels, starting from a uniform image, anordered-subsets expectation maximization (OS-EM) algorithm is performedusing only non-coincident singles data, and iterations are thencontinued using only coincidence data.

Other example methods and systems use a Bayesian projector function withnon-uniform emission probability along a line of response that isweighted by an a priori image generated from the low-resolution (Comptonkinematic collimation) channel to reconstruct the high-resolution(coincidence) channel, or vice versa. Another image reconstructionmethod uses priors generated by reconstructing images from high-spatialresolution coincidence data followed by post-reconstruction smoothing toprovide imaging.

Generally, an imaging system according to example embodiments of thepresent invention includes a plurality of 3-D detectors capable ofmeasuring the interaction position (e.g., in three dimensions) andenergies of individual photons emitted from a source, and a device orsystem for image reconstruction coupled to the one or more detectors.Examples of sources of emitted photons will be known to those ofordinary skill in the art. A nonlimiting example source of emittedphotons is animal tissue into which radioactive isotopes have beeninjected. The 3-D detectors are disposed with respect to the source ofemitted photons to receive the emitted photons and produce interactions.The emitted photons include single photons and coincidence photons.

The one or more detectors may include, as nonlimiting examples, 3-D PETdetectors and Compton cameras used in coincidence. Other suitabledetectors capable of measuring the position (in three dimensions) andenergies of individual photons emitted from the source may be used. Such3-D detectors have the ability to function as a coincidence detector andas a Compton camera, and can perform coincidence kinematics collimation.Nonlimiting examples of PET systems include systems having 3-Dpositioning cadmium-zinc-telluride (CZT) detectors. An example CZTdetector is described in International Patent Application No.PCT/US2005/035203, filed Sep. 30, 2005, which is incorporated in itsentirety by reference herein.

An image generator (that is, a device or system for imagereconstruction) is coupled to the 3-D detectors to receive a positionand energy for the produced interactions and reconstruct an image. Theimage generator is configured to generate a line projector functionbased on the coincidence photons and a cone-surface projector functionbased on the single photons. The image generator is further configuredto reconstruct an image using the generated line projector function andcone-surface projector function.

Examples of image generators include a computing device (as anonlimiting example, a PC or group of connected PCs) suitable forrunning an image reconstruction algorithm, which may be implemented insoftware, hardware, firmware, loaded via suitable media, etc. Acomputing device may include a suitable processor or processors, memory,input devices, storage devices, output devices (such as, but not limitedto, printers, monitors, network outputs, etc.), configured to receiveinputs directly or indirectly from the one or more detectors via anysuitable connection. According to example embodiments of the presentinvention, the computing device is configured to implement the imagereconstruction algorithm. Thus, additional embodiments of the presentinvention may be provided in a computing device configured to performmethods of the present invention and/or a computer-readable medium, apropagated signal, firmware, software, etc., capable of causing acomputing device to perform a method of the present invention.

It will be appreciated that various PET systems, including variouscommercial PET systems, capable of 3-D positioning may be used as theone or more detectors and image generator if configured to implementexample image reconstruction algorithms according to the presentinvention. Generally, the effectiveness of any such system will at leastpartly depend on the 3-D positioning resolution and energy resolution ofthe detectors used.

Embodiments of the present invention that image using coincidencephotons and single photons can improve the sensitivity, image quality,and/or quantification of PET. Example embodiments can reduce scan times,increasing patient throughput and reducing per-scan costs (andpotentially radioactive dosage delivered to the patient). Embodiments ofthe present invention may also be used to perform simultaneousmeasurements of PET and SPECT (single photon emission computedtomography) isotopes.

Preferred embodiments will now be discussed with respect to thedrawings. The drawings include schematic figures that are not to scale,which will be fully understood by skilled artisans with reference to theaccompanying description. Features may be exaggerated for purposes ofillustration. From the preferred embodiments, artisans will recognizeadditional features and broader aspects of the invention.

FIG. 1 shows an example imaging system 10. The imaging system 10includes a plurality of 3-D detectors 12 disposed with respect to asource 14 of emitted photons. A nonlimiting example 3-D PET detector 12is a 3-D cadmium zinc telluride (CZT) cross-strip detector. It will beunderstood, however, that methods and systems of the present inventionare also generally applicable to other 3-D detectors or Compton cameraswith coincidence capabilities. Semiconductor detectors, such as CZTdetectors, have an intrinsic resolution that is set by the pitch of anelectrode pattern deposited on the detector faces, rather than by usingarrays of crystal rods. Semiconductor detectors directly collect thecharge deposited by photon interactions, versus relying on scintillationlight creation, transport, collection, and photodetector conversion.

These 3-D detectors 12 are suitably coupled to an image generator 16,which receives signals from the 3-D detectors and processes the signalsto generate an image. Examples of suitable couplings will be understoodby those of ordinary skill in the art, including but not limited toelectrical and optical couplings. Examples of suitable image generators16 are described above. It is not required that the image generator 16be co-located with the 3-D detectors 12, but instead the image generatormay be located anywhere that signals from the 3-D detectors may bereceived.

Principles of example image reconstruction algorithms according toembodiments of the present invention will now be explained. Inconventional PET, images are reconstructed from coincidence events,which occur when exactly two photons are detected within a timecoincidence window. The projector function for a coincidence event isthe line between the two detectors that recorded the photons.

A 3-D PET detector such as the CZT detector 12, which can measure theposition and energy of individual interactions, can use Comptonkinematics to calculate a Compton kinematics cone-surface projectorfunction for non-coincident single photons. FIG. 2 shows an exampleindividual 3-D detector 12. In the CZT detector 12, orthogonal anode andcathode cross strip electrodes 20 disposed over a CZT crystal 21 areused to sample the interaction position of a photon 22 along twodimensions. The position of the interaction in the third dimension iscomputed from the anode-to-cathode signal ratio.

As a nonlimiting example, a 1 mm×1 mm×1 mm spatial resolution can beachieved by using 1 mm pitch anode and cathode orthogonal cross strips.The cross strip electrodes 20 provide effective detection elements thatcan resolve individual Compton scatter and photoelectric interactionswithin the detector with high energy resolution. In an example CZTdetector, energy resolution has been measured at ≦2.5% FWHM for 511 keVphotons. With high depth of interaction (DOI) resolution, the exampledetectors 12 may be brought in as close as desired for higher solidangle coverage and photon sensitivity. Further, example cross-stripdesigns allow a significant reduction in readout channels (e.g., 2n vs.n²) compared to an electrode design that achieves the same intrinsicresolution using an anode that includes a 2-D matrix of small squarepixels.

As shown in the example system of FIG. 1, the CZT detectors 12 may bestacked in an edge-on configuration. This allows incoming photons toencounter a minimum of multiple centimeters of detector material forhigh photon sensitivity. The edge-on orientation further facilitatesbetter coincidence time resolution, since the best timing performanceoccurs when the electron drift distance (orthogonal to electrode planes)is short and is generally better for thinner slabs. Reducing thethickness of the detector may reduce the effects of carrier drift time,but it will also increase the device capacitance, which also degradestime resolution for CZT (since there is no charge amplification).Performance of the detector will be affected by photon scatter betweenneighboring detector elements and the detector's Compton scatterperformance. Example CZT detectors 12 provide high intrinsic detectionefficiency and facilitate coupling to readout electronics.

With a minimum photon traversal distance of 4 cm, the single 511 keVphoton detection efficiency is roughly 86% (74% for two photons incoincidence). To preserve high photon sensitivity, if amulti-interaction photon event occurs, the event energy is determined bysumming charge deposited on any detector's strips within a localizedregion that is above a pre-defined threshold.

The example detector 12 configuration and arrangement can operate bothin coincident photon and Compton collimation (single photon) detectingmode. Example methods of the present invention apply these modes toprovide separate data channels for reconstructing images.

FIG. 3 illustrates how a high-resolution 3-D detector can calculate theincident angle of a single photon event. The incident angle of thephoton can be estimated when the position and energy of the first twointeractions in the detector are measured. Monte Carlo simulationssuggest that 70% of all detected events involve two or more interactionsin the detectors. A cone-surface projector function can be formed forthe single photon event where the line formed by the two interactionsfrom the cone axis and the cone half angle φ is calculated by

$\begin{matrix}{{\cos\;\varphi} = {1 - {m_{e}{c^{2}\left( {\frac{1}{E_{1}} - \frac{1}{E_{0}}} \right)}}}} & (1)\end{matrix}$where E₀ is the incident photon energy and E_(l) is the photon energyafter the first Compton interaction in the detector, m_(e) is the massof an electron, and c is the speed of light. Doppler broadening, energyblurring, and spatial blurring in the 3-D detector leads to angularblurring of the cone half angle φ. Compton collimation is describedfurther in, for example, D. B. Everett, J. S. Fleming, R. W. Todd, andJ. M. Nightingale, “Gamma-radiation imaging system based on the Comptoneffect,” Proc. IEE, vol. 124, pp. 995-1000, 1977; M. Singh, “Anelectronically collimated gamma camera for single photon emissioncomputed tomography, part I: theoretical considerations and designcriteria,” Med. Phys., vol. 10, pp. 421-427, 1983; and M. Singh and D.Doria, “An electronically collimated gamma camera for single photonemission computed tomography, part II: Image reconstruction andpreliminary experimental measurements,” Med. Phys., vol. 10, pp.428-435, 1983.

The forward model for reconstructing these single events is given as

$\begin{matrix}{{s\left( {y_{i},\phi_{i}} \right)} = {\int_{C}{{p\left( {\phi_{i},y_{i},x} \right)}{f\left( {x;T} \right)}\ {\mathbb{d}x}}}} & (2)\end{matrix}$where f(x)≡f(x;T) is a random variable corresponding to the number ofphotons generated over the total scan time T at the point x andp(φ_(i),y_(i),x) is the probability of an emission from position x intissue detected at y_(i) and incident angle φ_(i). Additionalinteractions (e.g., three or more) can result in additional informationderived via Compton kinematics.

By contrast, in conventional PET, a coincidence event occurs whenexactly two photons are detected in the photopeak energy window andcoincidence time window. For example, let y_(ki) correspond to the k-thand l-th detector pair, then the counts recorded for this pair is givenby

$\begin{matrix}{{o\left( y_{kl} \right)} = {\int_{L}{{p\left( {y_{kl},x} \right)}{f\left( {x;T} \right)}\ {\mathbb{d}x}}}} & (3)\end{matrix}$where f(x)≡f(x;T) is a random variable corresponding to the number ofphotons generated over the total scan time T at the point x andp(y_(kl),x) is the fraction of annihilation events at position x intissue that result in a pair of photons detected in coincidence recordedat the detector pair y_(kl). The discrete version of equation (2)provides an example of a projector function for single photon events,whereas the discrete version of equation (3) provides an example of aprojector function for coincidence events.

FIG. 4 shows an example imaging method for embodiments of the presentinvention using projector functions for both single photon events andcoincidence events. In an example imaging method, the emitted photonsource 14 generates annihilation photons in pairs, which may be detectedby the 3-D detectors 12. For example, during a decay event (step 40),measured using a preset coincidence time window, emitted photons aredetected (step 42) as photon interactions within the one or moredetectors, and at least one position (individual location) and energy ofinteraction is recorded. When the time window is completed (step 44),the energy of recorded photon interactions within the time window iscombined (step 46) (as a nonlimiting example, summed), and adetermination is made (step 48) as to whether a photon pair (acoincidence) has been detected and if so, whether one of the detectedphoton pair is scattered.

Preferably, as shown in FIG. 5, a determination is made based on thecombined amount of interaction at a particular detector location withinthe time window by comparing (step 50) the energy to a threshold. As anonlimiting example, for photons detected in coincidence, photoninteraction may take place at two distinct detector locations. If,within the time window, two photons are detected, each having combinedphoton interaction energy of, for example, 511 keV, or within apredetermined window surrounding 511 keV (step 52), it is determined(step 54) that coincidence photons have been detected.

If coincidence photons are detected, but one of the photons has combinedphoton interaction energy of less than 511 keV, or is outside thepredetermined window (step 56), then in some example embodiments it maybe determined (step 58) that a single-scatter coincidence event occurred(i.e., that one of the pair of photons scattered in tissue). In anexample embodiment, such single-scatter coincidence photons may beprocessed according to methods described in application Ser. No.12/154,261, entitled “METHOD AND SYSTEM FOR USING TISSUE-SCATTEREDCOINCIDENCE PHOTONS FOR IMAGING”, filed on even date herewith. In otherexample embodiments, scattered photons may be discarded.

However, if a single photon is detected, with combined photoninteraction energy of 511 keV, or within a window surrounding 511 keV(step 60), a single photon event is determined (step 62). If, on theother hand, a single photon, or both of a pair of coincidence photons,is detected with a combined photon interaction energy of less than 511keV (or an energy outside a predetermined window), the event may bediscarded (step 66).

Given the detected interactions in the detectors, including theinteraction position and energy, projector functions are used to providecollimation data channels (step 70). For example, if a coincidence eventis determined (step 54), a line projector function may be produced basedon the interaction location and energy for the two detected photons,providing a coincidence collimation data channel. If, on the other hand,a single photon event is determined (step 62), a cone-surface projectorfunction may be produced based on the interaction location and energyfor two or more interactions in a detector, providing a Comptonkinematics collimation data channel. The coincidence collimation channeldata and the Compton kinematics collimation channel data are combined(step 72), and an image is reconstructed (step 74), providingmulti-channel tomography. The combining may take place before or duringimage reconstruction.

Any of various image reconstruction methods, including but not limitedto list-mode, sinogram-based, histogram-based, etc., methods, can beused to reconstruct the images. In a nonlimiting example embodiment ofthe present invention, a list-mode (LM) algorithm is used to reconstructthe images. In the list-mode approach, a histogram of the counts is notused. Instead, the measurementsm={m_(i)},m_(i)ε{o(y_(ij)),s(y_(k),φ_(k))} correspond to the sequence ofindividual detected events. The expectation maximization algorithm (EM)can be used to reconstruct the image with voxels λ_(j) using theiteration

$\begin{matrix}{\lambda_{j}^{l + 1} = {\frac{\lambda_{j}^{l}}{n_{j}}{\sum\limits_{i}\;\frac{m_{i}p_{ij}}{\sum\limits_{k}\;{p_{ik}\lambda_{k}^{l}}}}}} & (4)\end{matrix}$where l is the previous iteration number, n_(j) represents thesensitivity correction for the j-th voxel, and p_(ij) represents thediscrete weights of the projector function for the j-th voxel andmeasurement m_(i). If m_(i) is a non-coincident singles event, thenp_(ij) is calculated from the discrete version of equation (2).Otherwise, m_(i) is a coincidence event, and a discrete version ofequation (3) is used to form p_(ij). This algorithm is readily adaptedfor list mode data, though equation (4) may also be implemented, forexample, as a sinogram or histogram-based algorithm. Nonlimitingexamples of list mode algorithms are provided in L. Parra and H. H.Barrett, “List mode likelihood: EM algorithm and image qualityestimation demonstrated on 2-D PET,” IEEE Trans. Med. Imaging, pp.228-235, 1998; and S. J. Wilderman, N. H. Clinthorne, J. A. Fessler, C-HHua, and W. L. Rogers, “List mode EM reconstruction of Compton scattercamera images in 3-D,” Proceedings of the 1998 IEEE Nuclear ScienceSymposium, vol. 3, pp. 1716-1720, 1998.

Ordered subsets can accelerate the image reconstruction algorithmprocess to form a list mode ordered subset EM algorithm (LM OS-EM). Inthis approach, the list-mode data set is divided into S equal lengthdata sets. The image is then updated after each subset before the nextdata subset is processed. Each iteration pass through the entire dataset then results in S image updates, accelerating the reconstructionprocess. An example of ordered subsets is provided in H. M. Hudson andR. S. Larkin, “Accelerated image reconstruction using ordered subsets ofprojected data,” IEEE Trans. Med Imaging, vol. 13, pp. 601-609, 1994.

For each list-mode count, a coincidence time window is applied followedby a clustering method to group interactions. Each cluster correspondsto the energy deposited by a single photon. Next, an energy window isused to reject photons that may have been scattered in tissue. If twoclusters are accepted after the energy window, sequence estimation isused to identify the first interaction for each photon. The coincidenceline projector function is used for p_(ij), with the ends of the linesegment positioned at the location of the first interaction for eachphoton.

For non-coincident single photon events, sequence estimation is used toidentify the first two interactions. The first two interactions are thenused to calculate the Compton kinematics projector function, forming thevalues of p_(ij) used by equation (4).

Coincidence events form one data channel with high-reconstructed spatialresolution. The non-coincident singles events form a second channel withlow reconstructed spatial resolution. Example embodiments of the presentinvention combine these channels to produce an image with improvedquality in terms of contrast, resolution, and/or signal-to-noise ratio.

Two example methods for combining the data channels include use ofsimultaneous data channels and sequential data channels, respectively.In a simultaneous data channel approach, the Poisson-distributed datavector is a combination of coincidence and non-coincident singles eventsgiven by

$\begin{matrix}{m = \begin{pmatrix}{o\left( y_{ij} \right)} \\{s\left( {y_{k},\phi_{k}} \right)}\end{pmatrix}} & (5)\end{matrix}$

The system matrix is then formed by discrete approximations to equations(2) and (3).

In a sequential data channel approach, the coincidence andnon-coincident singles events are used separately in the reconstructionprocess. For example, starting from a uniform image, the OS-EM algorithmis performed using only the non-coincident singles data. OS-EMiterations are then continued using only the coincidence data. Only asingle iteration can be performed using this example approach.

Another approach for combining multiple collimation channels fortomographic image reconstruction is a Bayesian projector approach.Bayesian methods have been proposed that add a penalty function toincrease smoothness in a maximum likelihood approach. Example Bayesianprojector approaches according to embodiments of the present inventionprovide a projector function to improve sensitivity, image quality(e.g., as determined by signal-to-noise ratio, resolution, and/orcontrast), and/or quantification by reducing the noise amplificationassociated with tomographic image resolution.

Generally, imaging systems such as multi-collimation PET systems havemultiple methods of collimation with varying spatial resolution. Onenonlimiting example is an insert system, which places high spatialresolution detectors inside a conventional PET system with collimationchannels formed by coincidences between the different detector rings.Another example is a PET system, such as that described above, usinghigh spatial and energy resolution 3-D detectors made from cadmium zinctelluride (CZT) detectors, which can collect high-resolution coincidenceevents (i.e., collimate photon pairs) and use Compton kinematics forlow-resolution collimation of single photons.

Compton collimation of single photons can dramatically increase overallphoton sensitivity by making use of events that are discarded byconventional imaging (e.g., PET) systems. However, in Comptonkinematics, with current technology, angular blurring of the Comptoncollimation direction leads to lower spatial resolution than standardcoincidence photon collimation. Reconstructing images with coincidenceand single photons can provide higher effective photon sensitivity andreconstructed signal-to-noise ratio.

Example multi-collimation methods using a Bayesian projector areprovided according to embodiments of the present invention. ExampleBayesian projector methods are applicable to various imaging systems,including any multi-collimation PET system.

In PET, the decay of a radionuclide in a subject generates a pair ofphotons traveling in opposite directions along a line. Detectorssurrounding the subject measure the photons (location and energy), andthe projector function corresponds to the line defined by the twomeasured photons. This line projector function specifies the probabilityof the decay event occurring at various positions in 3-D space. For PET,this function is zero everywhere except at the points defined by theline. The decay probabilities are assumed to be equal at every point onthis line.

In a Bayesian method according to example systems and methods of theinvention, one or more priors, from any of various sources, is used tomodify (e.g., re-weight) the probabilities along the line such that theprobabilities are not equal everywhere along the line. The one or morepriors represent the probability of a decay event as a function of 3-Dspace. The Bayesian projector may then be implemented by, as anonlimiting example, multiplying the line function (probability as afunction of 3-D space) with the prior (also a probability as a functionof 3-D space). By contrast, current methods for radionuclide imagingassume that the probabilities along the line are uniform, which may notbe as robust to noise.

According to an example method of the present invention, as shown inFIG. 6 an a priori image (also referred to as a prior) is generated(step 90) for modifying a projector function. The prior may be of adifferent resolution, a different modality, etc. The prior may also befiltered before it is used to modify the projector function.

Example methods and systems then obtain measurement data (step 92), andgenerate a projector function (step 94) based on the obtainedmeasurement. A projector function for tomography may be determined usingany appropriate method. A particular example method includes measuringposition and energy for photon interactions for coincidence photonevents. The projector function may be determined using the measurements.For example, a line between the detection locations for the coincidencephoton events may provide the projector function.

The projector function is modified using the a priori image(s) (step96), and an image is reconstructed (step 98) using the modifiedprojector function. For example, using a Bayesian projector function,the line projector function may be multiplied by the a priori image tomodify the function. More particular example methods for modifying theprojector function are described below. Various imaging processingmethods and/or imaging modalities can be used to improve the performanceof the Bayesian projection function by improving the modeling accuracyof the prior image.

A system for performing Bayesian methods according to embodiments of thepresent invention includes a plurality of detectors disposed andconfigured to obtain measurement data, an image generator coupled to theplurality of detectors to reconstruct an image based on the obtainedmeasurement data, and a source of an a priori image. The image generatoris configured to generate a projector function using the obtainedmeasurement data, modify the generated projector function using the apriori image, and reconstruct the image using the modified projectorfunction.

According to example embodiments of the present invention, an imagegenerator may be provided by a computing device configured to implementthe image reconstruction algorithm, including generating a projectorfunction and modifying the projector function. The image generator maybe any of the example devices and systems described above, so long asthe image generator is configured to perform methods of the presentinvention, including generating a projector function and modifying theprojector function, or cause another device or system to do so.

In the system 10 shown in FIG. 1, the detectors 12 may provide theplurality of detectors for an example Bayesian approach, and the imagegenerator may be provided by the image generator 16. A source for one ormore a priori images may be provided by the detectors 12 and/or by otherdetectors or a separate source. Exemplary detectors (for the detectorsthat obtain measurement data and/or for generating an a priori image)include 2-D detectors in an insert system, such as a ring ofhigh-resolution 2-D PET detectors inserted into a larger ring oflower-resolution 3-D detectors, multi-modality detectors, etc.

The source for a priori images may be the same detectors, devices,and/or systems for image reconstruction as those used above, and/or maybe detectors and devices using other tomography techniques, incombination with suitable image generators. Other sources include add-onPET systems, such as high-resolution insert systems. However, it is tobe understood that detectors or a priori image sources that can be usedare not to be limited to those particular detectors, image sources, orcombinations thereof that are described herein. For example, ifparticular embodiments of the present invention directed to imagingusing a Bayesian projector do not rely on Compton kinematics collimationfor providing a data channel, devices and systems according to thepresent invention for performing such methods need not include adetector or a priori source capable of providing Compton kinematicscollimation.

Methods according to the present invention employing Bayesian projectorfunctions may also be performed in multi-modality systems. For example,X-ray computed tomography (CT) may be used to produce an anatomicalimage of a subject. For PET, the radionuclide resides in tissue, andthus an a priori image may be produced using a CT image, such that theprobability is zero at all the air cavities (but, not the lungs) in thebody and equal (or non-zero) for all other tissue. Another applicationto PET is to combine measurements of PET systems (e.g., PET insertsystems) that employ detectors of different sizes. For single photonemission tomography (SPECT), methods of the present invention can beused for dual collimated systems that combine mechanical collimationwith electronic collimation. Additionally, in SPECT, methods of thepresent invention can be used to combine multiple collimation imagingsystems. For example, multi-head SPECT systems that use collimators withdifferent resolutions and sensitivities can be combined to produceimages.

In a nonlimiting example method of the present invention using PET, amultichannel PET system using 3-D detectors collects two different types(channels) of measurements by coincidence collimation and Comptonkinematics collimation. In coincidence collimation, as explained above,photons are detected in pairs, and the decay event is assumed to haveoccurred somewhere along the line between the two detected photons. InCompton kinematics collimation, a single photon is detected in a 3-Ddetector. The position and energies of the individual interactions inthe 3-D detector are used to calculate the direction of the incidentphoton. Using this direction, the projector function corresponds to acone-surface, and it is assumed that the decay event occurred somewhereon this cone-surface with equal probability.

Thus, 3-D detectors capable of measurement by coincidence collimationand Compton kinematics collimation can provide both a detector and asource of an a priori image. The Compton kinematics collimation may beused to modify the coincidence collimation. Alternatively, thecoincidence collimation may be used to modify the Compton kinematicscollimation. As one example, the coincidence collimation channel couldbe reconstructed by standard methods using the line projector functionto produce a 3-D image. This 3-D image can be used to create a Bayesianprojector for reconstructing the Compton kinematics collimationmeasurements. The projector function for Compton kinematics collimationwould then be the cone-surface function (a probability function in 3-D)multiplied by the prior (treated as a probability function in 3-D).Alternatively, the Compton kinematics collimation data could bereconstructed to produce a prior used to create a Bayesian lineprojector function for reconstructing the coincidence collimationmeasurements.

An example Bayesian projector approach combining coincidence collimationchannels and Compton kinematics collimation channels will now bedescribed. A maximum likelihood estimation (MLE) approach can be used toreconstruct PET images for multi-collimation schemes. MLE effectivelyweights a combination of the collimation channels (such as single andcoincidence photon), deconvolving the lower spatial resolution (singlephoton) channel to match the high-resolution (coincidence photon)channel. The weight of the low-resolution channel is proportional to thesignal-to-noise after deconvolution. For sufficiently large resolutionmismatch between channels, the low-resolution channel is effectivelyassigned a small weight. The MLE combination yields comparable spatialresolution, bias, and variance from images produced by using thehigh-resolution channel alone, while significantly improving thesignal-to-noise ratio (SNR).

For example, in conventional image reconstruction, the line projectorfunction assumes that the probability of the emission event is uniformalong the line of response. In an example Bayesian projector approach,the non-coincident singles are used to generate a prior. Particularly,an a priori image from the non-coincident singles is used to re-weightthe line projector such that the probability along the line of responseis proportional to the expected activity. For example, let g(x)≡g(x;T)be the image prior, the probability that a photon is generated over thetotal scan time T at the point x. The Bayesian line projector functionfor coincidence data is then given by

$\begin{matrix}{{o\left( y_{kl} \right)} = {\int_{L}{{p\left( {y_{kl},x} \right)}{g\left( {x;T} \right)}{d\left( {x;T} \right)}\ {\mathbb{d}x}}}} & (6)\end{matrix}$

Similarly, a Bayesian projector function for a non-coincident singlesevent is given by

$\begin{matrix}{{s\left( {y_{i},\phi_{i}} \right)} = {\int_{C}{{p\left( {\phi_{i},y_{i},x} \right)}{g\left( {x;T} \right)}{f\left( {x;T} \right)}\ {\mathbb{d}x}}}} & (7)\end{matrix}$

For multi-channel tomography, one data channel is used to generate aprior that is used to modify the projector function for thereconstruction of the other channel. For example, the non-coincidencesingles data (low-resolution) can be reconstructed to produce the priorimage. The Bayesian projector is then used to reconstruct thecoincidence events (high-resolution), producing the final image.

In an experiment using methods of the present invention, Monte Carlosimulations were performed of PET systems built using cross-strip CZTdetectors. A phantom was simulated for a box-shaped small animal PETsystem built using cross-strip CZT detectors. It was assumed that thedetectors had a 1 mm×1 mm by 1 mm spatial resolution with 3% energyresolution FWHM for 511 keV photons. It was also assumed that the energyresolution FWHM was 3%*√{square root over (511/e_(pho))} where e_(pho)is the energy of the photon in keV. A schematic of this detectorarrangement 100 is shown in FIG. 7. The system has an 8 cm×8 cmtransaxial FOV. The axial length of the simulated system was 2 cm. Dataacquisition was simulated for 7 non-overlapping bed positions. Hitsfiles were generated of all the individual interactions within thedetectors. These files were processed to simulate the performance of thesystem.

A resolution phantom was simulated as a 5 cm diameter, water-filledcylinder with a single plane of spherical sources divided into fourquadrants. The spherical sources in each quadrant were 1, 1.25, 1.5, and1.75 mm in diameter with center-to-center separation that was twice thediameter of the spheres. A total of 0.2 mCi of activity was simulated.Images reconstructed using the coincidence data and non-coincidentsingles data are shown in FIGS. 8A-8B.

Images reconstructed using the same data set by example methods areshown in FIGS. 9A-9D. Reconstruction using only the coincidence data isshown in FIG. 9A. There is no discernable difference in the imagequality between the simultaneous channel (FIG. 9B), sequential channel(FIG. 9C), and coincidence-only (FIG. 9A) images. The noise structurefor the simultaneous channel approach differs from the coincidence-onlyreconstructed image. The noise structure is visually identical forsequential channel and coincidence-only image reconstruction. TheBayesian projector method (FIG. 9D) produced an image with improvedcontrast against the background compared to the other methods.

The mean and variance images were computed from twenty simulated trialsfor each of the methods. The mean images are shown in FIGS. 10A-10D. Theimage quality is comparable for coincidence-only (FIG. 10A),simultaneous channel (FIG. 10B), and sequential channel (FIG. 10C)images. The mean reconstructed image for the Bayesian projector method(FIG. 10D) shows a larger partial volume effect for the 1 mm spheres.

The variance-to-signal ratio was computed from 20 trials for regions ofinterest (ROI) drawn around the spheres on the center plane. The resultsare as follows: the coincidence-only reconstruction method exhibited avariance-mean ratio of 1.00, while the simultaneous channel, sequentialchannel, and Bayesian projector methods exhibited variance-mean ratiosof 0.93, 1.01, and 1.35, respectively. The simultaneous channel methodsshowed the best performance, and the Bayesian projector approach had theworst performance.

The peak-to-valley ratio was measured from the mean images and plottedfor the different reconstruction methods and shown in FIG. 11. Thepeak-to-valley ratios are shown for the various sized spheres. TheBayesian projector approach had a better peak-to-valley ratio for allsized spheres.

The resolution for the various methods was calculated by drawingprofiles through the various sized spheres in the mean reconstructedimage. A Gaussian function was fitted to the profiles, and the fullwidth at half maximum (FWHM) for the various sized spheres is plotted inFIG. 12. The Bayesian projector methods showed better contrast andresolution for all size spheres than the other methods, with a slightloss in signal-to-noise ratio. However, the images produced by theBayesian projector function depend on the quality of the image prior andthe phantom characteristics.

The low-resolution nature of this image leads to partial volume effectsfor the 1 mm spheres. This partial volume effect results in a lowerprobability of counts placed in the 1 mm spheres by the Bayesianprojector function. Consequently, the reconstructed activity in the 1 mmspheres was biased down proportionately to the partial volume effect ofthe reconstructed image used to generate the prior. Effectively, countswere “stolen” from the 1 mm spheres and placed in the other spheres.Misplaced counts could explain the observed decrease in thesignal-to-noise ratio for the Bayesian projector method.

Additional embodiments of the invention use priors generated byreconstructing images from high-spatial resolution coincidence datafollowed by post-reconstruction smoothing with a spatially varying 3-Dfilter function. Methods of the invention may also use a gradientanisotropic filter. According to another embodiment of the presentinvention, an example 3-D OS-EM algorithm is used with a prior-weightedCompton collimated projector to reconstruct the single photon data andthe conventional (unweighted) projector to reconstruct the coincidencephoton data.

In conventional image reconstruction, the emission probability isuniform along a line of response (LOR). In an example Bayesian projectormethod, by contrast, the probability along the LOR is weighted by aprior image; particularly, the LOR probability passing through regionsof high activity in the prior will have high probability relative toregions of low activity in the prior.

In the example Bayesian method described above, a low-spatial resolutionCompton collimated single-photon channel is used to produce a prior forweighting the high-resolution coincidence photon channel to provide aqualitative improvement in visual quality. In another example method,priors generated from the higher resolution coincidence photon data areused for reconstructing the low resolution single photon channel.

An example reconstruction algorithm for the latter method is shown inFIG. 13. An a priori image 101 is produced by filtering 102 ahigher-resolution image 104. This higher-resolution image isreconstructed from the coincidence photons 106. The prior 101 is used toweight a Compton collimated single-photon channel (lower-resolutionchannel) 107, providing a weighted low-resolution channel 108. In theexample method, the list-mode OS-EM algorithm 110 is used to iterativelycalculate an MLE solution 112 by simultaneous reconstruction of both the(unweighted) high-resolution channel 114 and the weighted low-resolutionchannel 108. A nonlimiting example uses a list-mode 3-D OS-EM algorithmwith 5 iterations and 10 subsets/iteration—the minimum number ofiterations-subsets to achieve 9:1 sphere:background ratio for 1.75 mmspheres.

In an example method, a 3-D spatially-varying filter was used:

$\begin{matrix}{{y\left( {i,j,k} \right)} = {\sum\limits_{l}\;{\sum\limits_{m}\;{\sum\limits_{n}\;{{{I_{A}\left( {i,j,k,l,m,n} \right)} \cdot {h\left( {{i - l},{j - m},{k - n}} \right)}}{x\left( {{i - l},{j - m},{k - n}} \right)}}}}}} & (8)\end{matrix}$where h is the filter kernel, x and y are the images before and afterfiltering, and the indicator function I_(A) is defined over the intervalA={|x(i,j,k)−x(i−l,j−m,k−n)|<α√{square root over (x(i,j,k))}+ε}  (9)

The parameter α tunes the filtering to the expected lesion contrast. Anexample image using both unweighted coincidences and weighted Comptoncollimation photons was produced by one iteration with five subsets ofthe 3D OS-EM algorithm (for 9:1 sphere:background ratio, 1.75 mmspheres).

A second filter that may also be used is a gradient anisotropicnon-linear diffusion filter. For example, an iterative filter may becreated from a discrete diffusion equation. Each time step in thediffusion equation corresponds to an iteration of the filter. The totalintensity of all pixels in the image was conserved at every time stepwith pixel intensity flowing to adjacent pixels. The diffusion rate andnumber of iterations can be used to control the degree of smoothness inthe filtered image, with more iterations and larger diffusion ratesproducing smoother images. An example discrete diffusion equation isgiven by

$\begin{matrix}{\frac{u_{i,j}^{t + {\Delta\; t}} - u_{i,j}^{t}}{\Delta\; t} = {{\frac{1}{\Delta\; x}\left\lbrack {E_{i,j}^{r}{\nabla_{E^{u_{i,j}^{t}}}{- W_{i,j}^{t}}}\nabla_{W^{u_{i,j}^{t}}}} \right\rbrack} + {\frac{1}{\Delta\; y}\left\lbrack {N_{i,j}^{t}{\nabla_{N^{u_{i,j}^{t}}}{- S_{i,j}^{t}}}\nabla_{S^{u_{i,j}^{t}}}} \right\rbrack}}} & (10)\end{matrix}$where u is the intensity of the pixel at (i,j) at time step t. Thediffusion coefficients in the north, east, south, and west directionsare given by N, E, S, and W at pixel (i,j), respectively, and take theform of

$\begin{matrix}{D_{i,j}^{t} = {g\left( \left| \left. \nabla_{D^{u_{i,j}^{t}}} \right|^{2} \right. \right)}} & (11)\end{matrix}$where D specifies the direction (N, E, S, or W). The Perona-Malik filter(e.g., as described in S-J Park et al, “A prototype of very highresolution small animal PET scanner using silicon pad detectors,” Nuc.Instrum. Meth. Phys. Res. A, 570 (3), pp. 543-555, 2007) varies thediffusion coefficient, 1 within the interior of regions and 0 at theboundaries, in order to smooth the image while preserving edges.

For Compton collimation, the lines of response form the surface of acone as shown in FIG. 3. The measured energy of the first interaction isused to determine the photon angle φ relative to the cone axis, the linedefined by the first two interactions. Uncertainty in the measuredenergy and the positioning of the cone axis leads to angular blurring.The angular blurring varies depending on the energy of the firstscattering interaction and the distance between the interactions.Low-energy and high-energy interactions will have the poorest angularresolution. Also, the closer the two interactions are to each other, theworse the angular resolution.

Event filtering was used to improve the spatial resolution of Comptoncollimation. Since angular resolution degrades rapidly below a 15-20degree scatter angle, single photons with detector scatter below 20 keVwere not used to improve the angular resolution. A minimum interactiondistance threshold was used to reduce the uncertainty of the cone axisposition. Single photons were used only when the distance between thefirst two interactions was greater than 1 cm. At 1 cm separation betweeninteractions, a 1 mm voxel size results in an angular error variance of3 degrees if the discretization error is uniformly distributed. Eventfiltering improves angular resolution, but also reduces the singlephoton sensitivity.

In a Monte Carlo simulation of an example system, an 8×8×2 cm³box-shaped system 120 as shown in FIG. 14 was simulated using 4×4×1/2cm³ 3-D CZT detectors with cross-strip anodes and cathodes. This exampledetector can position Compton scattering interactions within thedetector in three dimensions with 1.5-2.5% FWHM at 511 keV energyresolution. As shown in FIG. 14, the detector is oriented in an edge-onconfiguration for higher sensitivity so that incoming photons see aminimum of 4 cm of CZT. Simulations were performed using an idealizedenergy resolution modelΔe=0.025√{square root over (511e)}  (12)where e is the energy of the interaction in keV. This idealized energyresolution model assumes noiseless readout electronics. A more realisticmodel was also simulated, which assumed the readout electronics providedan additional keV FWHM Gaussian noise source to each energy measurementindependent of the interaction energy.

Two digital phantoms were simulated, as shown in FIGS. 15A-B. Thephantoms were each 7.5 cm high by 3 cm diameter cylinders with 1, 1.25,1.5, and 1.75 mm diameter spheres separated by twice the diameterorganized in four different quadrants in the center slice of thecylinder. A total of 500 μCi total activity was scanned with 5 bedpositions.

Phantom 1 was a 9:1 sphere:cylinder concentration (activity) ratio withidealistic energy resolution and 30 sec/bed position. After eventfiltering, 11 million Compton collimation single photons and 10 millioncoincidence photons were used for image reconstruction. A 10 nscoincidence time window and a 10% energy window at 511 keV forcoincidence and single photons were used. The energy resolution of theCZT detector was 2.5% at 511 keV. Since multiple interactions can occur,the energy window was chosen to be larger than is conventionally used inPET.

In phantom 2, the spheres are organized in three columns with 10:1, 5:1,and 3:1 sphere-to-cylinder activity ratios in the outer, middle, andinner columns, respectively. The scan time was 60 sec/bed position usingthe more realistic energy resolution model. After event filtering, thesimulation yielded 27 million Compton collimated single photon eventsand 21 million coincidence photons. Setting the minimum interactiondistance threshold threshold to zero, the number of available singleevents was 124 million. Thus, event filtering reduced the number ofusable single photon events by approximately 80%.

Results are shown in FIGS. 16A-B. FIG. 16A shows the reconstructed imagefrom coincidence events for phantom 1. Normalization/sensitivitycorrection was not used in the image reconstruction. The list-mode OS/EMalgorithm was used with 2 iterations, with 10 subsets per iteration.Subsets were divided by time with an equal number of counts for eachsubset. The image in FIG. 16B was produced by combining coincidenceevents and singles using 1 iteration, with 5 subsets. The Bayesian priorwas produced from coincidence data by using 5 iterations and 10subsets/iteration. The two filters described above by equations (8) and(9) were used.

Using the Bayesian projector to reconstruct singles and coincidenceevents improved the SNR in a region of interest (ROI) drawn within thecylinder by a factor of 10 for similar recovered contrast of thespheres. The SNR in the spheres also improved by approximately 20%, asmeasured by drawing ROIs in the center of every sphere.

The reconstructed images with sensitivity correction for phantom 2 (withmore realistic energy blur model) are shown in FIGS. 17A-B. A MonteCarlo simulation with 30 minutes of simulated scan time was used tocalculate the sensitivity correction. Gaussian smoothing was used. Theimage reconstructed from coincidence events is shown in FIG. 17A. Thisimage was produced by 2 iterations, with 10 subsets per iteration. Theimage in FIG. 17B was reconstructed using the Bayesian projector and 2iterations, with 6 subsets per iteration from combining coincidenceevents and singles. The Bayesian prior was produced from coincidencedata using 2 iterations, with 10 subsets per iteration. The Perona-Malikfilter was used for de-noising the prior.

There was no significant improvement in the SNR for the spheres atcomparable contrast as shown in FIGS. 18A-B. The SNR in the backgroundcylinder ROI was improved by about 20%.

To assess the effect of detector voxel size, the voxel size wassimulated at 0.025 mm, 0.5 mm, and 1.0 mm. The results of the sphere(lesion) SNR vs. contrast ratio for various iteration-subsets is shownin FIGS. 19A-B. There was no significant difference in reconstructedimage quality for the various detector voxel sizes, suggesting thatenergy resolution was the dominant component of angular blurring forCompton collimation. Improved angular resolution of Compton collimationshould in turn increase the benefits of imaging single photons.

It will be understood that, though a small animal system such as thatused in experiments described herein has high coincidence sensitivityand low single photon sensitivity, a human imaging system would havesignificantly higher relative single photon count rate and could yieldimproved image quality for combined coincidence and Compton collimationPET. With a large number of single photons, more aggressive eventfiltering could be used to improve Compton collimation spatialresolution.

Significant advantages of embodiments of the present invention includereduction of scanning time to increase patient throughput, and improvesensitivity, quantification, and image quality (as defined bysignal-to-noise ratio, resolution, contrast, and contrast recovery). Itwill be appreciated that various methods are possible for combiningcoincidence and Compton kinematics collimation via a Bayesian projector,and the present invention is not be limited to the particular methodsdescribed herein. The filters described herein are also intended to benonrestrictive. It will further be appreciated that methods of imagingusing Bayesian multi-collimation schemes are not limited to combiningcoincidence and Compton kinematics collimation. Applications of thepresent invention include nuclear imaging modalities such as (but notlimited to) PET.

While various embodiments of the present invention have been shown anddescribed, it should be understood that other modifications,substitutions, and alternatives are apparent to one of ordinary skill inthe art. Such modifications, substitutions, and alternatives can be madewithout departing from the spirit and scope of the invention, whichshould be determined from the appended claims.

Various features of the invention are set forth in the appended claims.

1. A method for producing an image comprising: obtaining measurementdata for a coincidence photon event; generating a line projectorfunction based on the obtained measurement data; obtaining additionalmeasurement data for a single detected photon from an event other thanthe coincidence photon event; generating a cone-surface projectorfunction based on the additional measurement data; combining data fromsaid generated line projector function and said generated cone-surfaceprojector function; reconstructing an image using said combined datafrom said line projector function and said generated cone-surfaceprojector function.
 2. The method of claim 1, wherein said generatingthe cone-surface projector function uses Compton kinematics collimation.3. The method of claim 1, wherein said generated line projector functionprovides a coincidence collimation channel and said generatedcone-surface projector function provides a Compton kinematicscollimation channel; wherein said reconstructing an image furthercomprises: combining data from the coincidence collimation channel andthe Compton kinematics collimation channel.
 4. The method of claim 3,wherein said combining comprises using data from the coincidencecollimation channel simultaneously with data from the Compton kinematicscollimation channel.
 5. The method of claim 3, wherein said combiningcomprises using data from the coincidence collimation channelsequentially with data from the Compton kinematics collimation channel.6. The method of claim 3, wherein said combining comprises using datafrom the coincidence collimation channel to reweight the cone-surfaceprojector function.
 7. The method of claim 3, wherein said combiningcomprises using data from the Compton kinematics collimation channel toreweight the line projector function.
 8. The method of claim 1, whereinsaid obtaining measurement data for a coincidence photon eventcomprises: producing a photon interaction in each of a pair ofdetectors; for each of the pair of detectors, determining a position andenergy of the produced photon interaction.
 9. The method of claim 1,wherein said obtaining additional measurement data for the singledetected photon comprises: producing at least two photon interactions ina detector; determining a position and energy of the produced at leasttwo photon interactions.
 10. The method of claim 1, wherein saidreconstructing an image uses an image reconstruction algorithm.
 11. Asystem for radiation-based imaging comprising: a plurality of 3-Ddetectors disposed with respect to a source of emitted photons toreceive the emitted photons and produce interactions, the interactionsdetecting at least coincidence photons from a coincidence photon eventand, additionally, single detected photons from events other than thecoincidence photon event; an image generator coupled to said pluralityof 3-D detectors to receive a position and energy for the producedinteractions and reconstruct an image; said image generator beingconfigured to generate a line projector function based on the detectedcoincidence photons and a cone-surface projector function based on theadditional single detected photons, combine data from the generated lineprojector function and the generated cone-surface projector function,and reconstruct an image using the combined data from the generated lineprojector function and the cone-surface projector function.
 12. Thesystem of claim 11, wherein the generated line projector functionprovides a coincidence collimation channel and the generatedcone-surface projector function provides a Compton kinematicscollimation channel; wherein reconstructing the image further comprises:combining data from the coincidence collimation channel and the Comptonkinematics collimation channel.
 13. The system of claim 12, wherein thecombining comprises at least one of using data from the coincidencecollimation channel simultaneously with data from the Compton kinematicscollimation channel, and using data from the coincidence collimationchannel sequentially with data from the Compton kinematics collimationchannel.
 14. The system of claim 12, wherein the combining comprises atleast one of using the coincidence collimation channel to reweight thecone-surface projector function, and using data from the Comptonkinematics collimation channel to reweight the line projector function.15. The system of claim 11, wherein said plurality of 3-D detectorscomprises cadmium zinc telluride (CZT) detectors.
 16. The system ofclaim 11, wherein said image generator comprises a computing device. 17.An image generator comprising: a computing device configured to performa method comprising: obtaining measurement data for a coincidence photonevent; generating a line projector function based on the obtainedmeasurement data; obtaining additional measurement data for a singledetected photon from an event other than the coincidence photon event;generating a cone-surface projector function based on the additionalmeasurement data; combining data from said generated line projectorfunction and said generated cone-surface projector function; andreconstructing an image using said combined data from said lineprojector function and said generated cone-surface projector function.18. The image generator of claim 17, wherein said obtaining measurementdata for a coincidence photon event comprises: receiving a signalgenerated from a produced photon interaction in each of a pair ofdetectors; for each of the pair of detectors, determining a position andenergy of the produced photon interaction.
 19. An apparatus forcontrolling a computing device comprising: a non-transitorycomputer-readable medium containing computer-readable instructions that,when read, cause a computer to perform a method comprising: obtainingmeasurement data for a coincidence photon event; generating a lineprojector function based on the obtained measurement data; obtainingadditional measurement data for a single detected photon from an eventother than the coincidence photon event; generating a cone-surfaceprojector function based on the additional measurement data; combiningdata from said generated line projector function and said generatedcone-surface projector function; and reconstructing an image using saidcombined data from said line projector function and said generatedcone-surface projector function.
 20. the apparatus of claim 19, whereinsaid obtaining measurement data for a coincidence photon eventcomprises: receiving a signal generated from a produced photoninteraction in each of a pair of detectors; for each of the pair ofdetectors, determining a position and energy of the produced photoninteraction.